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Confining materials to two-dimensional forms changes the behaviour of the electrons and enables the creation of new devices. However, most materials are challenging to produce as uniform, thin crystals. Here we present a synthesis approach where thin crystals are grown in a nanoscale mould defined by atomically flat van der Waals (vdW) materials. By heating and compressing bismuth in a vdW mould made of hexagonal boron nitride, we grow ultraflat bismuth crystals less than 10 nm thick. Due to quantum confinement, the bismuth bulk states are gapped, isolating intrinsic Rashba surface states for transport studies. The vdW-moulded bismuth shows exceptional electronic transport, enabling the observation of Shubnikov–de Haas quantum oscillations originating from the (111) surface state Landau levels. By measuring the gate-dependent magnetoresistance, we observe multi-carrier quantum oscillations and Landau level splitting, with features originating from both the top and bottom surfaces. Our vdW mould growth technique establishes a platform for electronic studies and control of bismuth’s Rashba surface states and topological boundary modes1,2,3. Beyond bismuth, the vdW-moulding approach provides a low-cost way to synthesize ultrathin crystals and directly integrate them into a vdW heterostructure. 

An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wave function has remained beyond experimental reach. Here, we directly image the excitonic wave function in reciprocal space by measuring the momentum distribution of electrons photoemitted from excitons in monolayer tungsten diselenide. By transforming to real space, we obtain a visual of the distribution of the electron around the hole in an exciton. Further, by also resolving the energy coordinate, we confirm the elusive theoretical prediction that the photoemitted electron exhibits an inverted energy-momentum dispersion relationship reflecting the valence band where the partner hole remains, rather than that of conduction band states of the electron. 

Resolving momentum degrees of freedom of excitons, which are electron-hole pairs bound by the Coulomb attraction in a photoexcited semiconductor, has remained an elusive goal for decades. In atomically thin semiconductors, such a capability could probe the momentum-forbidden dark excitons, which critically affect proposed opto-electronic technologies but are not directly accessible using optical techniques. Here, we probed the momentum state of excitons in a tungsten diselenide monolayer by photoemitting their constituent electrons and resolving them in time, momentum, and energy. We obtained a direct visual of the momentum-forbidden dark excitons and studied their properties, including their near degeneracy with bright excitons and their formation pathways in the energy-momentum landscape. These dark excitons dominated the excited-state distribution, a surprising finding that highlights their importance in atomically thin semiconductors.